Higher-order kinematical effects in deeply virtual Compton scattering

We study the deeply virtual Compton scattering cross-section in twist-two generalized parton distribution (GPD) approximation, and show that different choices of light-cone vectors and gauges for the final photon polarization will lead to different higher-order kinematical corrections to the cross-section formula. The choice of light-cone vectors affects kinematic corrections at the twist-three level, accounting for the differences between the cross-section formulas in the literature. On the other hand, kinematical corrections from higher-twist GPDs should eliminate the light-cone dependence at twist three. Those light-cone dependencies are studied systematically at JLab 12 GeV and future EIC kinematics. They serve as the intrinsic systematic uncertainties in extracting the Compton form factors through the cross-section formula. More importantly, they are also necessary for understanding cross-section measurements with higher-twist precision and to reconstruct higher-order Compton form factors.

Scattering and fusion phenomena of 6Li +209Bi system

In nucleus–nucleus collisions, the partial-wave scattering matrix, for the total effective complex potential is calculated, which explains the data of angular distribution of elastic scattering cross-sections. Furthermore the absorption cross-section is obtained from the arbitrarily small intervals which helps to derive the fusion cross-section ([Formula: see text]) data at different center-of-mass energies ([Formula: see text]) by collecting the absorption contributions in the interior region of the effective potential. Here, the potential is taken as energy independent and its weakly absorbing nature supports the resonance states in various partial-wave trajectories. Therefore, the resonances show oscillatory behavior changes with respect to energy [Formula: see text], which is the second derivative of the product [Formula: see text] with respect to [Formula: see text]. In this paper, we have successfully discussed the elastic scattering and fusion cross-sections simultaneously with the results of [Formula: see text].

2,6-/1,5-Naphthoquinodimethane bridged porphyrin dimer diradicaloids

2,6-Naphthoquinodimethane (2,6-NQDM)- and 1,5-naphthoquinodimethane (1,5-NQDM)-bridged porphyrin dimers, 2,6-P2 and 1,5-P2, were synthesized as relatively stable compounds. Both exhibit open-shell singlet ground state according to variable-temperature (VT) NMR and magnetic measurements, as well as restricted active space spin-flip (RAS-SF) calculations. The 1,5-P2 isomer has a larger diradical character ([Formula: see text], based on the RAS-SF calculations) and smaller singlet-triplet energy gap ([Formula: see text] kcal/mol, based on SQUID measurements) compared to the 2,6-P2 isomer ([Formula: see text], [Formula: see text] kcal/mol). In addition, 2,6-P2 shows intense one-photon absorption (OPA) ([Formula: see text] nm, [Formula: see text] M[Formula: see text] cm[Formula: see text] and a large two-photon absorption (TPA) cross-section ([Formula: see text] GM at 1400 nm) in the near-infrared region, while 1,5-P2 with larger diradical character displays red-shifted but weaker OPA ([Formula: see text] nm, [Formula: see text] M[Formula: see text] cm[Formula: see text] and a smaller TPA cross-section ([Formula: see text] GM at 1600 nm). Both compounds show four reversible redox waves and 1,5-P2 has a smaller electrochemical energy gap (1.06 eV vs.1.16 eV for 2,6-P2). Therefore, the bridge structure has a significant impact on the diradical character, electronic properties, and magnetic behaviors of the obtained porphyrin-based diradicaloids.

Systematic decay analysis of 202Po∗ compound nucleus using Dynamical Cluster-decay Model

The decay analysis of [Formula: see text]Po[Formula: see text] compound nucleus (CN), formed via [Formula: see text]Ca+[Formula: see text]Gd reaction, with inclusion of additional degrees-of-freedom, i.e., the higher multipole deformations, the octupole ([Formula: see text]) and hexadecupole ([Formula: see text]), the corresponding “compact” orientations ([Formula: see text]), and noncoplanarity degree-of-freedom ([Formula: see text]0), is investigated within the collective clusterization approach. The Quantum Mechanical Fragmentation Theory (QMFT)-based Dynamical Cluster-decay Model (DCM), wherein the point of penetration [Formula: see text], fixed via the in-built neck-length parameter [Formula: see text] in [Formula: see text] (equivalently, the “barrier lowering” [Formula: see text]), is used to best fit the channel cross-section ([Formula: see text]) and predict the quasi-fission (qf)-like nCN cross-section [Formula: see text], if any, and the fusion–fission ([Formula: see text]) cross-sections. We also look for other target-projectile (t-p) combinations for the synthesis of CN [Formula: see text]Po[Formula: see text].

Subjecting Dark Matter Candidates to the Cluster Test

Galaxy clusters, employed by Zwicky to demonstrate the existence of dark matter (DM), pose new stringent tests. First, the possibility is considered that merging clusters demonstrate that DM is self-interacting with cross-section [Formula: see text] 2[Formula: see text]cm2/gr. In that case, MACHOs, primordial black holes (PBHs) and light axions that build MACHOs are ruled out as cluster DM, while GeV and TeV WIMPs and keV sterile neutrinos are challenged. Next, recent strong lensing and X-ray gas data of the quite relaxed and quite spherical cluster A1835 are analyzed. These lensing data involve a covariance matrix of which the small eigenvalues have to be regularized. This is achieved with a new, general, parameter-free method: binning with respect to a model fit, and accounting for intra-bin fluctuations. This method allows to test the cases of DM with Maxwell–Boltzmann, Bose–Einstein and Fermi–Dirac (FD) distribution, next to Navarro–Frenck–White profiles. Fits to all these profiles are formally rejected at over [Formula: see text], except in the fermionic situation. The interpretation in terms of pseudo-Dirac neutrinos with mass of [Formula: see text][Formula: see text]eV/[Formula: see text] is consistent with results on the cluster A1689, with the DM fractions from WMAP, Planck and DES, and with the non-detection of neutrinoless double [Formula: see text]-decay. The predicted mass will be tested in the KATRIN and PTOLEMY experiments.

Simulation of the Field Emission from a Hemisphere-on-Post Nanowire: Revision of the Fowler–Nordheim Formula in Terms of Nonuniformity and Resistance

The electric field on a hemisphere-on-post nanowire is numerically calculated using the finite element method (FEM). The FEM calculation results show that the field is sufficiently strong for extracting a significant field emission current only in a small area at the top of the hemisphere, while the contribution to the field emission from the other part of the hemisphere and the flank side of the cylinder is negligible owing to the rapid drop of the electric field. Both the local current density at the top of the hemisphere ([Formula: see text]) and the average current density across the nanowire cross-section ([Formula: see text]) are calculated and the [Formula: see text]-to-[Formula: see text] ratio ([Formula: see text]) is introduced to reflect the nonuniformity of the field emission. An empirical formula with proper parameters that can best fit the simulation results is derived for describing the dependence of [Formula: see text] on the macroscopic electric field ([Formula: see text]). As a result, the [Formula: see text]–[Formula: see text] relationship is attained and the revision to the traditional Fowler–Nordheim (FN) formula caused by the nonuniformity of field distribution is found in both the pre-exponent part and the exponent part, so that the deviation of the FN plots from linearity often observed in experiments is partly accounted for. Moreover, the resistance at the emitter-substrate interface is shown to cause saturation in the field emission current and a downward bending of the FN plot in the high-field region.

Left and right regular elements of the semigroups of transformations preserving an equivalence relation and a cross-section

Let [Formula: see text] be the semigroup of all transformations on a set [Formula: see text]. For an arbitrary equivalence relation [Formula: see text] on [Formula: see text] and a cross-section [Formula: see text] of the partition [Formula: see text] induced by [Formula: see text], let [Formula: see text] [Formula: see text] Then [Formula: see text] and [Formula: see text] are subsemigroups of [Formula: see text]. In this paper, we characterize left regular, right regular and completely regular elements of [Formula: see text] and [Formula: see text]. We also investigate conditions for which of these semigroups to be left regular, right regular and completely regular semigroups.

The influence of a strong infrared radiation field on the conductance properties of doped semiconductors

This work presents an analytic angular differential cross section formula for the electromagnetic radiation field-assisted electron scattering on impurities in semiconductors. These impurities are approximated with various model potentials. The scattered electrons are described with the well-known Volkov wave function, which has been used to describe strong laser field matter interaction for more than half a century, which exactly describes the interaction of the electron with the external oscillating field. These calculations show that the electron conductance in a semiconductor could be enhanced by an order of magnitude if an infrared electromagnetic field is present with 1011 W/cm2 < I < 1013 W/cm2 intensity.

Fractal planetary rings: Energy inequalities and random field model

This study is motivated by a recent observation, based on photographs from the Cassini mission, that Saturn’s rings have a fractal structure in radial direction. Accordingly, two questions are considered: (1) What Newtonian mechanics argument in support of such a fractal structure of planetary rings is possible? (2) What kinematics model of such fractal rings can be formulated? Both challenges are based on taking planetary rings’ spatial structure as being statistically stationary in time and statistically isotropic in space, but statistically nonstationary in space. An answer to the first challenge is given through an energy analysis of circular rings having a self-generated, noninteger-dimensional mass distribution [V. E. Tarasov, Int. J. Mod Phys. B 19, 4103 (2005)]. The second issue is approached by taking the random field of angular velocity vector of a rotating particle of the ring as a random section of a special vector bundle. Using the theory of group representations, we prove that such a field is completely determined by a sequence of continuous positive-definite matrix-valued functions defined on the Cartesian square [Formula: see text] of the radial cross-section [Formula: see text] of the rings, where [Formula: see text] is a fat fractal.